TEUI L.2 Heating and Cooling Degree Days

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Heating and Cooling Days (HDD and CDD, respectively) are an effective shorthand for defining climate-related impacts on heating and cooling loads of buildings. The idea is simple enough, but the units – a mashup of time and temperature – are abstract, and so difficult to reconcile with our experience. In its simplest form, the higher a HDD value (ie. 7,000, typical in a sub-arctic or Northern location) the more heating energy is generally required. A lower value means there is less of a Heating Demand, like in Toronto with a typical HDD value at around 3,800.

In order to calculate Heating Demand from HDD values, one needs to know the average R-value (Resistance) or U-value (Transmission) of an entire building, which considers every surface bounded by exterior Air (Ae), and a weighted average of its surface and U-value to arrive at an aggregate total. In Passivhaus a rule of thumb for a kind of national average one should aim for the value is a U-value of 0.15 or lower, this isn’t a KPI of PHPP, but it bodes well for hitting the aggressively low TEDI value of 15kWh/m2/yr. The equation then considers how much thermal energy is lost through the envelope to Ae, as the difference between the desired temperature inside (ie. 22ºC), and the actual temperature outside (which can vary every hour of every day).

The equation itself is pretty simple (thanks to Dr. Ted Kesik for this one!): HEDI Ae =(HDD*Average U-Value*24)/1000, Where HEDI Ae is the Heating Energy Demand Intensity per m2 of envelope area (NOT floor area) facing Ae or exterior Air, multiplied by 24 hours and divided by 1000 to go from kKh/yr to hours for the purpose of getting a value in kWh/m2 instead of Watt-days/m2. This is basically the rate at which thermal energy is transmitted through the building envelope per unit area. The higher the HEDI, the crummier the envelope, basically.

Once you have that value, you multiply it by the total area facing outside air (Ae) generally walls including windows and roofs and maybe overhanging floor areas, and that gives you the heating season heatloss through the envelope, one of many losses to consider in the total picture of the building. The higher the transmission of energy, the higher the U-value. The higher the U-value, the faster energy is transmitted away (wasted) and the higher the heat-loss and thus heating load.

More examples: Let’s say the envelope was perfectly insulated, and so had a U-value of zero. Then you would have an equation that looks like this: HEDI Ae = (3,800*0*24)/1000=0. Your heatloss is effectively zero, and so your heating load is effectively zero. Then let’s take a really lousy U-value of 1: HEDI Ae = (3,800*1*24)/1000=91.2 kWh/m2, you can see I have a really high transmission value for HEDI. If I doubled my insulation value, I would halve my U-value, so I’d get a U-value of 0.5, let’s see the effect: HEDI Ae = (3,800*0.5*24)/1000=45.6 kWh/m2, half the heatloss of my U-value of 1. This is how OBJECTIVE calculates the rate of transmission and the heatloss through the envelope using HDD and conversely CDD values. But where do these HDD and CDD values come from, and how are they calculated? The first question is easy to answer, the HDD and CDD values for most locations in Canada are defined in a table in the proposed 2025 NBC (Building Code). The CDD values are new, because we will have a new requirement for cooling with a setpoint of 24ºC. More on that over here: https://openbuilding.ca/2024/07/07/teui-b-1-major-occupancy/

We choose a baseline temperature, like 18ºC, the most common heating season baseline as it represents a kind of low-end of a thermostat’s set-point for heating, or the temperature below which some form of heating would be required. One hour of outside weather at 17ºC, would then result in one degree-hour of heating, or one hour where a heating system might be required to bring a building up to 18ºC. The idea of a degree day is just 24 hours of these differences between the exterior temperature and the 18ºC set-point. It’s easier to show this as a table, so let’s make one:

Hour	01	02	03	04	05	06	07	08	09	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
Degrees Outside in ºC	-7	-8	-9	-9	-10	-10	-11	-11	-10	-9	-8	-7	-6	-5	-5	-6	-7	-8	-8	-9	-9	-10	-10	-10
Degrees below 18ºC	25	26	27	27	28	28	29	29	28	27	26	25	24	23	23	24	25	26	26	27	27	28	28	28

So this table basically represents the temperature difference between outside and desired interior temperature for a single day in January, in Toronto, Canada. To get a single ‘Heating Degree Day’ value for this day, there are two methods, and when we want the HDD for a whole year, we just add the HDD values for every day. The two methods are a simplified, or traditional one, and a more advanced one which is arguably more accurate, and it has to do with the frequency of the temperature sample or the time interval. Let’s start with the first method, which comprises just two data-points, a high and a low.

The simplified Tmax-Tmin method estimates Heating Degree Days (HDD) by using daily maximum (Tmax) and minimum (Tmin) temperatures for outside:

1. Calculate the average daily temperature: (Tmax+Tmin)/2
2. Find the difference between this average temperature and the base temperature (typically 18°C).
3. If the average temperature is below the base, the difference is the HDD value for the day. If above, HDD is zero (because if above 18ºC there is no heating energy required!).

For the above day:

1. Tmax = -5°C, Tmin = -11°C
2. Average = (−5+−11)/2=−8°C
3. HDD = 18−(−8)=26

That’s how you get the HDD value for just one day in the Toronto Heating Season. The full heating season is generally considered to be about 245 days long, from about Mid-September when the weather starts to cool, right up to Mid-May when the Robins start returning. To get Heating Degree Days (HDD) for the whole year or the whole heating season, we do the same little equation for every day of the year and add them up. For Toronto, the HDD fluctuates between 3,500 and 4,000 annually, with 3,800 being an average in that range. It is important to note that this difference from year to year is about 12.5%, which can impact heating loads by the same amount, and even more when we have an extremely warm or cold year. This is one of many reasons it is important to remember any energy model targets an average, within a range of possibilities and can never be predictive of a real year, unless the exact HDD value for that specific year is entered into the equations.

Conversely, the Cooling Season is about 120 days long, from about June to September. We know there are 4 actual seasons, but from the perspective of your heating and cooling systems, there are only 2. With climate change, we are seeing an increase in Cooling Season total days (from 120 to about 140 days) and a reduction in Heating Season total days (from 245 down to 225). This shift means more cooling load than we have had historically, but also less heating load, which means we need to carefully plan for future cooling loads, and not to oversize heating systems.

OBJECTIVE TEUI3 uses HDD values from a baseline temperature of 18ºC (interior) for its calculations, based on the revised (proposed draft 2025 NBC PCF) Table C2 in the National Building Code of Canada. This revised table has HDD and CDD values for almost every municipality in Canada. This is the 5th tab or worksheet in the Excel version of the OBJECTIVE tool.

Similar to the calculation method for HDD, CDD are derived by considering a temperature above which a cooling system would be required to bring values down to. This Tset for Cooling is generally the same 18ºC, but a cooling degree day is ‘triggered’ when the average values for that day are above 18ºC, rather than below 18ºC as is the case with HDD. However, the simplified method for calculation can mislead us into believing there are no cooling degree hours in a given day, or more that if we took the 24hr average instead of just the Tmax-Tmin averages, where we would find the cooling system would be called to run more, or less, depending on the day in question. Here’s an example.

Hour	01	02	03	04	05	06	07	08	09	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24
Degrees Outside in ºC	17	17	17	16	16	16	17	18	20	22	23	24	24	23	22	21	20	19	19	18	17	17	17	16
Degrees above 18ºC	00	00	00	00	00	00	00	00	02	04	05	06	06	05	04	03	02	01	01	00	00	00	00	00

The better way to calculate Heating and Cooling Degree Days, is to take the hour-by-hour average from the 24hr period, rather than just the Tmax-Tmin. The difference can be substantial.

Imagine we have 23 hours at 18ºC, and then a big swing up to 24ºC, the min-max method would skewer the data to show a value of 21 degree-hours, when in fact the 24hr averaged value is 18.25 degree-hours, a much lower value, and a more accurate one given the period under consideration, since we didn’t need to run cooling for those 23 out of 24 hours of the day!

For the CDD table above, the Tmin-Tmax method arrives at 2 Degree-Hours for the day noted, where the 24hr average method shows 1 Degree-Hours for the same day. Here’s the simplified version below:

Tavg=(24+16​)/2 = 20°C

CDD=Tavg−baseline=20−18 = 2 Degree-Hours

Now let’s consider the hourly average method.

(17+17+17+16+16+16+17+18+20+22+23+24+24+23+22+21+20+19+19+18+17+17+17+16)/24=19ºC

CDD=Thourly-avg−baseline=19−18 = 1 Degree-Hour

While this difference may seem trivial for a single day, consider that the total cooling degree hours for Toronto is anywhere from 275.8 (historically) to 486.9 (future weather), if there was a difference of 1-degree hour for every day of the cooling season, the total variation could be as high as 120-140 degree days of seasonal difference, which on a cool year (120 days) could be as much as +/-44% and on a hot year (140 days) as much as +/-29%. The over-or under-estimating is a function of the hourly temperature average versus the Max-Min methods for CDD and HDD calculations, as well as the total number of CDD and HDD which is changing with our changing climate.

This trivial math difference could result in the significant over-or under-sizing of heating and cooling equipment. While this is one of the reasons the static calculation methods using HDD and CDD may be considered inferior to dynamic hourly energy modelling methods that carefully consider losses and gains based on combinations of cloud cover, radiation, temperature, etc. for every one of the 8760 hours per year. But we argue that static calculations could be better if we considered the 24hr average method to obtain HDD and CDD, rather than using the traditional Min-Max method.

If you have gotten this far, Bravo! But you may be questioning, who decides these things, and what are the conventions, and what are the sources of the weather data in any case since there can be such a huge resulting variability in the energy loads as a function of these sources? Well, generally in Canada we have Environment Canada providing us with excellent weather data for past, present and future conditions. For our purposes HDD and CDD values are always from a Base temperature of 18ºC. The tables in the older building codes (2020 and before) drew on data from much older weather files, and in some cases for calculating peak heating cooling loads, the data goes back as far as 1951! ASHRAE is the body that defines how HDD and CDD values are calculated. But the truth is, the more data points one uses in terms of the time intervals for HDD and CDD values, the more closely these will approximate real-world loads.

Here’s how Claude AI explains it:

This is a great observation about the difference between daily and hourly averages. Let me explain why this happens and then show how to handle it correctly.

Heating Degree Day Calculation Examples

The difference you’re observing occurs because of a mathematical principle known as Jensen’s inequality and the non-linear nature of heating degree day calculations. Here’s why:

1. Daily Temperature Patterns:
   • Temperatures typically follow a daily cycle (cooler at night, warmer during day)
   • When you average daily temperatures, you lose this variation
   • This matters because heating degree days use a threshold (typically 18°C)
2. Why the Results Differ:
   • If temperature varies above and below the base temperature within a day
   • The hourly calculation captures every hour below the threshold
   • The daily average might be above the threshold, missing the heating needs during cold hours

For example, imagine a day where:

• 12 hours at 10°C
• 12 hours at 20°C
• Daily average = 15°C
• Base temperature = 18°C

Using daily average:

• 15°C average means 3 heating degree days (18-15)

Using hourly values:

• 12 hours need 8 degrees of heating (18-10)
• 12 hours need 0 degrees of heating (20>18)
• Average = 4 heating degree days

The more variable your temperatures are, the larger this difference will be. For accurate heating degree day calculations, it’s better to:

1. Calculate HDDs at the hourly level
2. Sum these up to get daily values
3. Then calculate averages if needed

• Here’s some research from Rutgers University: https://climate.rutgers.edu/stateclim/?section=menu&%20target=calculating_daily_mean_temperature
• Here’s an excellent site from the ClimateAtlas.ca for HDD values (historical and future): https://climateatlas.ca/map/canada/hdd_2060_85#
• ClimateAtlas.ca for CDD values (historical and future): https://climateatlas.ca/map/canada/cooldd_2060_85#